What can be learned from the historical trend of crude oil prices? An ensemble approach for crude oil price forecasting

Crude oil price series are nonlinear and highly volatile, making it difficult to obtain satisfactory performance for traditional statistical-based forecasting methods. To improve forecasting accuracy, this study proposes a novel learning paradigm by integrating the trajectory similarity method with machine learning models based on the decomposition-ensemble framework. In the proposed learning paradigm, raw data of international crude oil prices are first decomposed using variational mode decomposition (VMD), after which, using sample entropy (SE), the resulting essential modal functions are divided into high and low frequencies. The process aims to reorganize the data by using the forecasting properties of different models. Finally, to obtain the final forecasting results, two models, i.e., the trajectory similarity method (TS) and long short term memory neural network (LSTM), are applied to predict and sum up the low and high-frequency subseries, respectively. As sample data for validation, this study selected the international crude oil price series of West Texas Intermediate (WTI) and Brent. Experimental results showed that the proposed VMD-SE-TS/LSTM learning paradigm significantly outperforms all other benchmark models, including the single models without decomposition and the hybrid models with decomposition. The proposed approach performs best in different evaluation metrics and statistical tests under different horizons, indicating that the proposed VMD-SE-TS/LSTM learning paradigm is effective and robust in crude oil price forecasting.